Problems with the determination of elastic constants from higher-order surface waves: Results for Al on NaCl

Using Brillouin scattering we have studied the surfacelike generalized Lamb modes in Al films on NaCl. Using a theory in which the elastic constants ($C_{\mathrm{ij}}$) of Al are taken from bulk values, reasonably good agreement is found for the positions of the peaks. However, we were unable to fit our experimental results to obtain the $C_{\mathrm{ij}}$ independently, since different combinations of the $C_{\mathrm{ij}}$ lead to similar spectra and dispersion curves. The changes in the spectra brought about by varying each one of the $C_{\mathrm{ij}}$ are investigated theoretically, but in no case could the experimental linewidths be reproduced. The fact that the experimental linewidths are much narrower than the calculated ones is very hard to explain unless it is assumed that the Al films are not completely bonded to the substrate. Calculations on unsupported films support this explanation. Our results clearly show the difficulty in obtaining information on elastic constants from an analysis of generalized Lamb modes of a film on a substrate and illustrate some of the problems which can be encountered.